Cleaning apparatus of the kind specified make use of strip-shaped cleaning elements equipped with wiper blades or of rod-shaped cleaning elements equipped with sponge-like or lambskin-like coverings. The surface to be cleaned is wetted with cleaning fluid by means of the cleaning elements equipped with such coverings, while the strip-shaped cleaning elements equipped with wiper blades wipe the fluid off the surface to be cleaned. If a cleaning apparatus is equipped with these two kinds of cleaning elements, all that the operator needs to do for the two successive jobs is merely to turn the cleaning apparatus through 180.degree.. It is true that such cleaning elements are attached releasably to a handle of varying length, but the attaching means are not adapted to the rapid and frequent interchange of cleaning elements.